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Reduction with Respect to the Effective Order and a New Type of Dimension Polynomials of Difference Modules

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Alexander LevinAuthors Info & Claims

ISSAC '22: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation

Pages 55 - 62

https://doi.org/10.1145/3476446.3535497

Published: 05 July 2022 Publication History

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Abstract

We introduce a new type of reduction in a free difference module over a difference field that uses a generalization of the concept of effective order of a difference polynomial. Then we define the concept of a generalized characteristic set of such a module, establish some properties of these characteristic sets and use them to prove the existence, outline a method of computation and find invariants of a dimension polynomial in two variables associated with a finitely generated difference module. As a consequence of these results, we obtain a new type of bivariate dimension polynomials of finitely generated difference field extensions. We also explain the relationship between these dimension polynomials and the concept of Einstein's strength of a system of difference equations.

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Cited By

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Levin A(2024)New Difference Gröbner Bases and Bivariate Difference Dimension PolynomialsMathematics in Computer Science10.1007/s11786-024-00589-818:3Online publication date: 24-Jul-2024
https://doi.org/10.1007/s11786-024-00589-8
Levin A(2023)Generalized characteristic sets and new multivariate difference dimension polynomialsApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-023-00628-035:1(31-53)Online publication date: 28-Oct-2023
https://doi.org/10.1007/s00200-023-00628-0

Index Terms

Reduction with Respect to the Effective Order and a New Type of Dimension Polynomials of Difference Modules
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Algebraic algorithms

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Abstract
We introduce a new type of characteristic sets of difference polynomials using a generalization of the concept of effective order to the case of partial difference polynomials and a partition of the basic set of translations $σ$ . Using properties of ...

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ISSAC '22: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation

July 2022

547 pages

ISBN:9781450386883

DOI:10.1145/3476446

General Chair:
Marc Moreno Maza
University of Western Ontario, Canada
,
Program Chair:
Lihong Zhi
Chinese Academy of Sciences, China

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 05 July 2022

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ISSAC '22: International Symposium on Symbolic and Algebraic Computation

July 4 - 7, 2022

Villeneuve-d'Ascq, France

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Levin A(2024)New Difference Gröbner Bases and Bivariate Difference Dimension PolynomialsMathematics in Computer Science10.1007/s11786-024-00589-818:3Online publication date: 24-Jul-2024
https://doi.org/10.1007/s11786-024-00589-8
Levin A(2023)Generalized characteristic sets and new multivariate difference dimension polynomialsApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-023-00628-035:1(31-53)Online publication date: 28-Oct-2023
https://doi.org/10.1007/s00200-023-00628-0

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Wronskian type determinants of orthogonal polynomials, Selberg type formulas and constant term identities

Multivariate difference-differential dimension polynomials and new invariants of difference-differential field extensions

Generalized characteristic sets and new multivariate difference dimension polynomials

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Wronskian type determinants of orthogonal polynomials, Selberg type formulas and constant term identities

Multivariate difference-differential dimension polynomials and new invariants of difference-differential field extensions

Generalized characteristic sets and new multivariate difference dimension polynomials

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